"FRODO LIVES!" I read these words in 1966, written high up on the wall in the New York subway. JRR Tolkien had become a cult figure for the counter-culture, long before Hollywood adaptations turned his lively tales into heaps of golden treasure, but it wasn't until much later that it became clear to me that Frodo was a relative of Bilbo Baggins, hero of The Hobbit, a children's book published in 1937, and that in the mid-1950s Frodo's adventures had been published, in three volumes, as The Lord of the Rings.

However, while I didn't know Frodo in 1966, I did know the name of JRR Tolkien. He had been Oxford's professor of Anglo-Saxon since 1926, and then Merton professor of English, retiring in 1959, just before I arrived. In three years in Oxford, I never heard of him as the creator of Bilbo and Frodo, only as the interpreter of, and authority on, the great Old English epic poem Beowulf. His British Academy lecture of 1936, "Beowulf: The Monsters and the Critics", was the first to treat the poem as a poem, not as an ancient monument of interest to antiquarians. We students also read his preface to Clark Hall's literal prose crib of Beowulf.

Christopher Tolkien, JRRT's third son and his literary executor, has now edited a volume of his father's writings on Beowulf comprising a translation, an extended commentary and two fictions deriving from the poem, each surviving in two forms. He tells us that he first heard of Beowulf and the golden hall of Heorot more than 80 years ago, when his father sang him "The Lay of Beowulf", a ballad of his own composing. At that time, the future editor was seven or eight years old. It is quite something for a son to publish his father's work in the son's 90th year. So this volume is itself extraordinary, but even if it wasn't, it would be an object of curiosity to Tolkien fans, since Beowulf – although an epic not a romance – is at the root of the romances that have brought him his following. In The Lord of the Rings, the episode of the Riders of Rohan derives directly from the poem, as do the orcs and much else, though the ring itself does not. The commercial success of Tolkien and CS Lewis, whose work at Oxford immersed them in medieval literature, has founded a fantasy fiction industry. And this fantasy fiction, as Terry Pratchett observed, is full of junk from Tolkien's attic, junk that, simplified and multiplied, is the currency of the gaming industry and of books and TV series such as Game of Thrones.

Exactly what Tolkien's fiction fans will make of these six texts I do not know. To adapt the story of the curate's verdict on his bishop's egg: all parts of this book are good, but some are drier than others. Two of the works are of thorough professional scholarship, while the others are the product of artistic and linguistic invention. These reflections were composed or prepared for the personal use, interest or enjoyment of the author, not of the public. A partial exception to this is the commentary, a selection from the lectures that Tolkien gave to generations of (often unwilling) undergraduates in the English school.

Throughout his life, the professor of Anglo-Saxon was keener to publish his creative than his academic work. Indeed, Christopher Tolkien has already brought out nine works unpublished at the author's death in 1973, not to mention a history of Middle-earth in 12 volumes. But while this new book is from Tolkien's attic, it is not junk. The six texts in this volume exist in overlapping drafts, which pose problems for an editor, even an editor who at the age of 16 typed out the first half of his father's translation of Beowulf. This editorial task has been done with scrupulous care.

"It is well known that there exists a translation of Beowulf into modern English prose made by JRR Tolkien," says the preface, adding "that it has remained unpublished for so many years has even become a matter of reproach". The existence of a JRRT translation may have been quite well-known. I had heard of its existence. But I assumed that it would not be in prose but in verse, since in 1961 or 1962 Christopher Tolkien had shown me an extract from a verse translation by his father. At the time I had been commissioned by Penguin to translate into modern verse a selection of Old English poetry, including some extracts from Beowulf. Nevill Coghill, the Penguin translator of Chaucer, had encouraged my translations, and had sent me to see the younger Tolkien. To my surprise, Christopher Tolkien produced from inside his jacket some typed pages of a version by his father. It was in a verse form that imitated that of the original – as did my own versions, originally stimulated by the example of Ezra Pound's version of "The Seafarer". Christopher Tolkien wondered whether imitative verse could work well with modern English.

My versions appeared in Penguin Classics in 1966 as The Earliest English Poems, followed a few years later by a verse Beowulf. They take their place in a tradition of verse translations that includes those of Edwin Morgan and Seamus Heaney, as well as William Morris and the lines of Beowulf that Tennyson translated when he was an undergraduate. Hundreds of translations of Beowulf have been published, nine of them into Japanese. One of the English ones is by the Scott Moncrieff who translated Proust. Most of them are in prose.

This "new" Tolkien translation, originally composed in 1926, is in a prose that sticks as closely as possible to the meaning and clause-order of the original. It has great accuracy and a sense of rhythm. Its style is, like that of the original, archaic, and often has striking inversions of word-order. It has its own spell, though its movement is more crabbed than that of the equally accurate version made by GN Garmonsway in 1968. Short extracts do not fairly represent translations of long works, but Tolkien will have taken much care with the last lines of the poem: "Thus bemourned the Geatish folk their master's fall, comrades of his hearth, crying that he was ever of the kings of earth of men the most generous and to men most gracious, to his people most tender and for praise most eager."

The felicities of Tolkien's version will be evident only to readers familiar with the Anglo-Saxon original. This may also be true of the commentary on the text, the extracts from which in this book are more than twice as long as the 100-page translation. The commentary shows the depth of Tolkien's knowledge of the languages and early literatures of north-west Europe. It is a privilege to observe such a deeply scholarly and imaginative mind at work on what it loved best.

These two long and learned texts are followed by four short invented texts. "Sellic Spell" (Marvellous Tale) is a speculative recreation in prose of the folk-tale that, Tolkien thought, may have preceded Beowulf before it took its present more "historical" form. Then follows a partial retelling of the same story – in Old English – composed by Tolkien. Finally, "The Lay of Beowulf", sung to Christopher by his father, is a rhymed ballad in the style of "The Lady of Shalott". Tolkien's Lay has a refrain which employs "Heorot" in the same way that Tennyson employs "Shalott".

Christopher Tolkien presents his compilation as "a memorial", a portrait of a mind. That mind possessed a linguistic scholarship and a literary imagination very rarely found together. I salute the editor's pietas, but I am more interested in Beowulf than in Tolkien. This may put me in a minority among buyers of the book. For me, there is more interest in what the book says about Beowulf, and Tolkien's bold recreations of earlier stages of the poem's composition than what it tells us of Tolkien. This is surely what JRRT would have wished.

• Michael Alexander's Beowulf: A Verse Translation is published by Penguin. To order Beowulf: A Translation and Commentary for £16 with free UK p&p call Guardian book service on 0330 333 6846 or go to guardianbookshop.co.uk.